The Kentucky Republican said the legislation would be stripped of language attacking President Obama’s 2014 executive actions on immigration. That move has set up a fight with House Republicans, with fewer than 80 hours to the DHS shutdown deadline.

McConnell said he would be willing to vote on the clean measure before considering a separate bill that would prohibit the administration from implementing Obama’s executive actions shielding the immediate family members of citizens and permanent legal residents from deportation.

“Unless the Speaker is in on the proposal — of course we have to make sure that we can get a bill to the president, not that we send a hot potato to Boehner,” Reid said.

“That doesn’t do the trick,” he said of McConnell’s proposal.

It is far from clear that Boehner can win a majority of House Republican votes for a clean Homeland Security funding bill. The Speaker is scheduled to hold a crucial meeting of his conference Wednesday morning.

“The Speaker has been clear: The House has acted, and now Senate Democrats need to stop hiding. Will they continue to block funding for the Department of Homeland Security or not?” said Michael Steel, Boehner’s spokesman.

Asked whether his boss warned Boehner of the new tack, McConnell spokesman Don Stewart said, “I don’t have any readouts about their meetings. They update each other all the time.”

The GOP leaders have different considerations. McConnell has his eye on November 2016 and retaining his new majority in the upper chamber against a tough map. Boehner isn’t worried about losing the House, which would require Democrats to win 30 seats; what he has to worry about is igniting another Tea Party revolt that has previously threatened his Speakership.

Reid’s statement sparked exasperation among Republicans.

“Apparently inspired by President Obama’s own over-reach, Sen. Reid is now shamelessly threatening to filibuster a clean Homeland Security funding bill,” said a senior GOP House aide.

By withholding their support, Democrats can extend the fight in an issue where the clock is now firmly on their side. McConnell’s move suggests he fears his party would take the bigger political hit from a shutdown.

He conceded Tuesday that he did not know how the GOP-led House would react.

“I don’t know what the House will do but I do think we have a responsibility to act here,” McConnell said.

McConnell hopes House Republicans will be placated by his strategy to force Senate Democrats to vote on the 2014 immigration order. It would need 60 votes to pass the Senate, and seven Democrats are on record questioning Obama’s decision to circumvent Congress to protect millions of illegal immigrants.

It appears unlikely that most of those Democrats would back the Republican bill, but it could be a tough vote.

Conservative groups pushed Boehner on Tuesday to reject McConnell’s plan, with Heritage Action for America announcing it would count any vote for a clean bill as a negative mark on its legislative scorecard.

“The House of Representatives acted wisely, properly, funding Homeland Security and not allowing activities to be carried out that are unlawful and that Congress has rejected,” Sessions said. “Now, there are some even on the Republican side that say, ‘Oh, gosh, you know the president will blame us even if it’s not our fault and we might as well cave in and give him what he wants.’ ”

Other Senate Republicans, however, urged Boehner to embrace McConnell’s plan.

In a statement later released by his office, he called the new strategy a “mistake.”

“Leadership’s current plan — to pass clean DHS funding and separate legislation barring executive amnesty — is a mistake. Congress is obliged to use every constitutional check and balance we have to rein in President Obama’s lawlessness, and that includes both our confirmation authority over nominees and the power of the purse.”